document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1108784>Question 1108784</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have $100000 to invest at 4% interest.if you wish to withdrawal equal annual payments for 4 years, how much couid you withdrawal each year and leaves $0 in the investment account? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724016 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=724016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 100,000 is invested at 4% interest peryear.\r<BR>\n" );
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document.write( "you wish to withdraw money at the end of each year, for 4 years and have 0 in the account at the end of the fourth year.\r<BR>\n" );
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document.write( "your withdrawal amount would be equal to 27,549.00454 each month.\r<BR>\n" );
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document.write( "the year by year calculations are shown below:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2018/020905.jpg\" alt=\"$$$\" >\r<BR>\n" );
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document.write( "the calculation of the withdrawal was done using the TI-BA-II financial calculator.\r<BR>\n" );
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document.write( "in this calculator, the entries were made as follows:\r<BR>\n" );
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document.write( "N = 4<BR>\n" );
document.write( "I/Y = 4 (% is assumed by the calculator).<BR>\n" );
document.write( "PV = -100,000 (no comma)<BR>\n" );
document.write( "FV = 0\r<BR>\n" );
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document.write( "then 2nd PMT gets you the withdrawal amount.\r<BR>\n" );
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document.write( "the calculator shows the withdrawal as 27,549.00454.\r<BR>\n" );
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document.write( "that's a rounded number.\r<BR>\n" );
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document.write( "the actual number goes out for more digits.\r<BR>\n" );
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document.write( "the excel printout uses a similar formula, only it carries out the result to more decimal digits.\r<BR>\n" );
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document.write( "the formula in excel is =PMT(rate,nper,pv,[fv],[type])\r<BR>\n" );
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document.write( "if fv is 0 and type is end of time period payments/withdrawals, then the formula used can be PMT(rate,nper,pv), which is what i used, because fv is assumed to be 0 and end of time period payments are assumed.\r<BR>\n" );
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document.write( "there is also a manual formula that can be used to calculate the withdrawal.\r<BR>\n" );
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document.write( "that formula is shown below:\r<BR>\n" );
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document.write( "ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "a = (p*r)/(1-(1/(1+r)^n)) \r<BR>\n" );
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document.write( "a is the annuity.<BR>\n" );
document.write( "p is the present amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods. \r<BR>\n" );
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document.write( "with this formula:\r<BR>\n" );
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document.write( "a is what you want to find.<BR>\n" );
document.write( "p is the present amount = 100,000 (without the comma).<BR>\n" );
document.write( "r is the interest rate per year = .04 (not the interest rate percent).<BR>\n" );
document.write( "n is the number of year = 4\r<BR>\n" );
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document.write( "formula of a = (p*r)/(1-(1/(1+r)^n)) becomes:\r<BR>\n" );
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document.write( "a = (100000*.04)/(1-(1/(1+.04)^4)) \r<BR>\n" );
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document.write( "solve for a to get a = 27549.00454.\r<BR>\n" );
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document.write( "when you enter the formula in your calculator, make sure the parentheses are entered exactly as shown in the formula.\r<BR>\n" );
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document.write( "your solution, rounded to 2 decimal digits, is that you would withdraw 27,459.00 at the end of each year.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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